As the scaling rate \(c_N\)  of statistic (REF ) is unknown, we follow an approach similar to the feasible EVT REF  and use a second intermediate order statistics to eliminate \(c_N\) .There are alternative approaches to inference using intermediate order statistics. For example, the subsampling approach
of [1]}, [2]} can be used to account for unknown scaling rate \(c_N\) . However, the presence of a slowly varying component in \(c_N\)  requires using multiple subsampling sizes, which may be problematic if \(N\)  is not extremely large.
Alternatively, for example, see ch. 4 of [3]} for inference under a second-order condition in a setting without estimation noise.
By using a pair of statistics which converge to the same random variable, we can exploit a knife-edge bias created by the difference in scaling factors.
The following theorem first establishes that such a technique works in the noiseless case, which may be of independent interest; the result is then transferred to noisy observables.
